Write the standard form of each equation. Then graph the equation.
x^2+y^2+6x-8y+18=0
Answers
The standard form of the equation is (x + 3)² + (y - 4)² = 2.
What is standard form of equation?A linear equation with two variables has the conventional form Ax + By = C, where A, B, and C are constants and where A and B are not equal to zero. The general form of a linear equation is another name for this format. When the line is plotted on the Cartesian plane, the constant term C and coefficient A in this form indicate the line's y-intercept and slope, respectively. When solving systems of linear equations and graphing linear equations, the standard form is helpful.
Complete the squares for the given equation: x² + y²+ 6x - 8y + 18=0.
Starting with the x terms, we add (b/2)² to both sides of the equation:
x² + 6x + 9 + y² - 8y + 18 = 9
For y terms by adding (c/2)² to both sides of the equation:
x² + 6x + 9 + y² - 8y + 16 = -2
The standard form is:
(x + 3)² + (y - 4)² = 2
Hence, the standard form of the equation is (x + 3)² + (y - 4)² = 2.
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Related Questions
will give brainiest if correct and quick
Answers
Answer: -2， 6
（-2）Because from 3a³ to (1)a³, it needs to subtract 2a³.
(6) Because from -5b³ to b³, it needs to add 6.
An inverse variation includes the points (5, 3) and (1, n). Find n.
Write and solve an inverse variation equation to find the answer.
n=
Submit
Answers
Answer:
n = 15
Step-by-step explanation:
the equation for inverse variation is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the point (5, 3 ) , that is y = 3 when x = 5 , then
3 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )
15 = k
y = [tex]\frac{15}{x}[/tex] ← equation of variation
substitute (1, n ), that is x = 1, y = n into the equation
n = [tex]\frac{15}{1}[/tex] = 15
What is a rectangular prism?
A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.
The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.
How do I find the volume of a rectangular prism?
The rectangular prism volume formula is:
volume = h × w × l,
where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:
Find the box length. For example, it can be equal to 18 in.
Determine its width. Let's say you measured 12 in.
Find out the rectangular prism height. Assume it's 15 in.
Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.
How do I find the area of a rectangular prism?
The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:
surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),
where h is prism height, w is its width, and l is its length.
Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:
Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².
Or save yourself some time and use our rectangular prism calculator.
Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.
How do I calculate the diagonal of a rectangular prism?
To determine the diagonal of a rectangular prism, apply the formula:
diagonal = √(l² + h² + w²)
where h is prism height, w is its width, and l is its length.
Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.
How to calculate volumes of the other solids?
That rectangular prism was a piece of cake! If you are amazed at how easily you can calculate the volume with our tool, try out the other volume calculators:
triangular prism calculator
cylinder volume calculator
sphere volume calculator
cone volume calculator
pyramid volume calculator
Answers
Triangle MNO and triangle PQR are shown on the coordinate plane.
R
Q
P
321
11
10
9
8
7
6
10
D
3
2
-
M
-14-13-12-11-10-9-8-7-6-5-4-3-2-10 1 2
OF NOT
-2
N
N
3
O
x↑
4 5
What sequence of transformations proves AMNO APQR?
OAMNO was dilated by a factor of 3 about the origin, then reflected across the x-axis to form APQR.
OAMNO was dilated by a factor of 3 about from the origin, then reflected across the y-axis to form APQR.
OAMNO was dilated by a factor of 4 about the origin, then rotated 180° clockwise about the origin to form APQR
OAMNO was dilated by a factor of 4 about the origin, then translated left 7 units to form APQR
Answers
The correct sequence of transformations that proves AMNO and APQR are congruent is: OAMNO was dilated by a factor of 3 about the origin, then reflected across the y-axis to form APQR.
The sequence of transformations proves AMNO APQRThe correct sequence of transformations that proves AMNO and APQR are congruent is:
OAMNO was dilated by a factor of 3 about the origin, then reflected across the y-axis to form APQR.
To see why, let's examine the properties of the two triangles:
Triangle MNO has vertices at (-2,-1), (-2,4), and (3,1).
Triangle PQR has vertices at (-6,-3), (-6,12), and (9,3).
If we dilate triangle MNO by a factor of 3 about the origin, we get a new triangle with vertices at (-6,-3), (-6,12), and (9,3). This is because each coordinate of MNO is multiplied by 3:
(-2,-1) -> (-6,-3)
(-2,4) -> (-6,12)
(3,1) -> (9,3)
If we reflect this new triangle across the y-axis, we get a new triangle with vertices at (6,-3), (6,12), and (-9,3). This is because the x-coordinates of each point are negated:
(-6,-3) -> (6,-3)
(-6,12) -> (6,12)
(9,3) -> (-9,3)
This final triangle, with vertices at (6,-3), (6,12), and (-9,3), is congruent to triangle PQR. Therefore, we have shown that AMNO and APQR are congruent.
This theorem relates to theorems previously studied in the sense that it involves transformations of geometric shapes, which is a fundamental concept in geometry. In real-world applications, these transformations can be used in computer graphics, architecture, and engineering, among other fields, to manipulate and analyze shapes and structures.
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Colin invests £980 into his bank account. He receives 6% per year simple interest. How much will Colin have after 7 years? Give your answer to the nearest penny where appropriate.
Answer:
Explanation:
Solving steps:
Answers
Colin have £ 1392 in his bank account after 7 years.
Step-by-step explanation:
Given, Principal = P = £ 980
Rate of interest = R = 6% = = 0.06
Time = T = 7 years
Amount = A = P + S.I
Simple Interest = S. I = PRT = 980 x 0.06 x 7 = £ 411.6
Amount after 7 years = £ 980 + £ 411.6 = £ 1391.6 ≈ £ 1392
Hence, Colin have £ 1392 in his bank account after 7 years.
Drag the similar figure into the table. Angle measures are rounded to the nearest integer.
Answers
Triangle (B) is a comparable number that you must drag into the table.
What are angles?
An angle is formed when two straight lines or beams meet at a singular endpoint.
The intersection of two locations is known as the vertex of an arc.
The word "angle" is derived from the Latin word "angulus," which means "corner."
But there are some basic viewpoints.
Combining different shots greatly expands your camera options.
The most confusing of the five angles involves taking a scene from straight overhead.
So, the following:
Using the provided figure, we obtain:
A 60-degree equilateral triangle is depicted in the image.
And as can be seen in figure B, we obtain an equilateral triangle with a 60-degree inclination on each side.
Therefore, triangle (B) is a comparable number that you must drag into the table.
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Pearl's Plumbing initially estimated the cost to fix Terrell's sink at $450. Fortunately for
Terrell, the prediction was 12.5% more than the actual cost. What was the actual cost of the
repair?
Answers
According to the given data the actual cost of the repair was $393.75.
What is meant by estimated cost?Estimated cost refers to the approximate amount of money that is expected to be spent on a particular project, task, or item. It is a prediction of the expected cost based on the available information and assumptions about the project or item being estimated. Estimated costs can be based on various factors such as labor, materials, equipment, overhead, and other expenses.
According to the given information:If the estimated cost was 12.5% more than the actual cost, then the actual cost was 100% - 12.5% = 87.5% of the estimated cost.
Let x be the actual cost of the repair. Then, we can set up the following equation:
87.5% of estimated cost = actual cost
0.875 * 450 = x
Solving for x, we get:
x = $393.75
Therefore, the actual cost of the repair was $393.75.
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The graph shown here is the graph of which of the following rational functions?
O A. F(x) = 1/X2
O B. F(x) = 1/(x-2)(x+1)
O C. F(x) = 1(x+2)(x-1)
Answers
The equation of the rational function is F(x) = 1/(x-2)(x+1). Thus, the answer is B. F(x) = 1/(x-2)(x+1).
What is a rational function?It is a type of function that can be expressed in the form f(x) = p(x) / q(x), where p(x) and q(x) are polynomials and q(x) is not equal to zero. Rational functions are used in various areas of mathematics, including calculus and algebra.
The graph of a rational function is the set of points which satisfy the equation of the rational function.
In this case, the equation of the rational function is F(x) = 1/(x-2)(x+1).
The graph of this function is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.
The graph of a rational function can be determined by finding the zeroes, vertical and horizontal asymptotes, and intercepts of the function.
The zeroes of F(x) = 1/(x-2)(x+1) are x = 2 and x = -1. The vertical asymptote is x = 0 and the horizontal asymptote is y = 0.
The intercepts are (2, 0) and (-1, 0).
The graph of F(x) = 1/(x-2)(x+1) is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.
This is different from the graph of F(x) = 1/X² which is a parabola and from the graph of F(x) = 1(x+2)(x-1) which is two lines intersecting at (2, 0) and (-1, 0).
Therefore, the correct answer is B. F(x) = 1/(x-2)(x+1).
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principle amount =750 interest rate =5% time = 4 years
how much interest is gained after 4 years ?
Answers
Answer:
Step-by-step explanation:
use formula I = prt
I=Interest P=principal R=rate T=time so Interest is = to 750 x 5% or 0.05 x 4 which is 150 so after 4 years 150 interest is gained
Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
Answers
a) the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles, is 0.0889 or approximately 0.089.
b) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.
c) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.
d) the probability that the selected consumer is 35-55 years old or likes Crunchicles is 0.44 or 44%.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
To solve these problems, we need to use the information given in the table and apply the rules of conditional probability and total probability.
What is the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles?
We want to find P(18-24 | disliked). By Bayes' theorem, we have:
P(18-24 | disliked) = P(disliked | 18-24) * P(18-24) / P(disliked)
We know that P(disliked | 18-24) = 17/132, P(18-24) = 92/300, and P(disliked) = 150/300. Therefore,
P(18-24 | disliked) = (17/132) * (92/300) / (150/300) = 0.0889
So the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles, is 0.0889 or approximately 0.089.
What is the probability that the selected consumer dislikes Crunchicles?
We want to find P(disliked). We know that the total number of consumers surveyed is 300 and the number of consumers who disliked Crunchicles is 105. Therefore,
P(disliked) = 105/300 = 0.35
So the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.
What is the probability that the selected consumer is 35-55 years old or likes Crunchicles?
We want to find P(35-55 or likes). By the rule of total probability, we have:
P(35-55 or likes) = P(35-55) + P(likes)
We know that P(35-55) = 32/300 and P(likes) = 92/300. Therefore,
P(35-55 or likes) = 32/300 + 92/300 = 0.44
So the probability that the selected consumer is 35-55 years old or likes Crunchicles is 0.44 or 44%.
Hence, a) the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles, is 0.0889 or approximately 0.089.
b) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.
c) the probability that the selected consumer dislikes Crunchicles is 0.35 or 35%.
d) the probability that the selected consumer is 35-55 years old or likes Crunchicles is 0.44 or 44%.
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Rosa and Clarice have left over bread (not including the end pieces), so they decided to make sandwiches for the librarian, office staff, and custodian. How many sandwiches will they be able to make?
Answers
The number of sandwiches Rosa and Clarice can make depends on the amount of leftover bread they have.
To determine the number of sandwiches that Rosa and Clarice can make, we need to know how much bread they have.
Let's assume that they have 10 slices of bread left over. To make a sandwich, you typically use two slices of bread, so we can make 5 sandwiches with 10 slices of bread.
However, if they have more or less bread, the number of sandwiches they can make will change accordingly.
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According to the graph, what is the value of the constant in the equation below?
Answers
According to the graph, the value of the constant in the equation below is 2. The correct option is B.
What is constant in a graph?A constant function in mathematics is one whose (output) value is constant regardless of the input value.
We are given the equation for the height.
On the graphic, height, and width are related. By choosing a point, we can find the value of the constant.
To find a constant in a graph, the width is multiplied by height.
(Height)(Width) = Constant.
Multiply any of the coordinate values shown, and you will see the constant is 2.
3 × 1.5 = 2 × 1 = 8 × 4 = 7 × 3.5 =
we will take only one variable which is 2 x 1 = 2, so the constant is 2
Therefore, the correct option is B, 2.
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Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69.1 bpm. For a random sample of 128
adult males, the mean pulse rate is 67.8 bpm and the standard deviation is 11.2 bpm. Complete parts (a) and (b)
below.
a. Express the original claim in symbolic form.
bpm
(Type an integer or a decimal. Do not round.)
b. Identify the null and alternative hypotheses.
bpm
Но
H₁:
bpm
(Type integers or decimals. Do not round.)
Answers
a) The original claim in symbolic form would be: H0: μ = 69.1
b) Ha represents the claim that the mean pulse rate is not equal to 69.1.
What is null hypothesis?
A null hypothesis is a statement that there is no significant difference or relationship between two variables in a study or experiment. It is the default or initial position that is assumed to be true until evidence proves otherwise.
a) The original claim in symbolic form would be:
H0: μ = 69.1
Where μ represents the population mean pulse rate of adult males.
b) The null and alternative hypotheses can be stated as:
Null hypothesis: H0: μ = 69.1
Alternative hypothesis: Ha: μ ≠ 69.1
Where Ha represents the claim that the mean pulse rate is not equal to 69.1.
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I need help on this one
Answers
Answer:
19 degrees
Step-by-step explanation:
hope this helps
Geometry!
Use the figure below to solve for x
Answers
What is the principal square root of -27
Answers
the principle square root of -27 is √5.196.
please help me i need to get these right
Answers
The value of x in the right angled triangle above is 7√3.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.
To calculate the value of x in the right angle triangle above, we use the formula below.
Formula:
tan∅ = opp./adj.Where:
∅ = Included angle = 30°opp. = Opposite = 7adj. = Adjacent = xtan30° = 1/√3Substitute these values into equation 1 and solve for x
tan30° = 7/xx = 7/tan30°x = 7/(1/√3)x = 7√3
Hence, the value of x is 7√3.
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Jessie bought some pizzas and burgers. 3/4 of the food bought were burgers. Jessie bought 18 burgers. How many pizzas and burgers did Jessie buy altogether?
Answers
Answer:
24
Step-by-step explanation:
Total number of food = x
If ¾ of food = number of burgers bought
Then 3/4 times x = 3x/4
3x/4= 18
x = 24
pleasee and thank you very much
Answers
The average rate of change between t = 0 and t = 2 is 16 feet/second and the average rate of change between t = 1 and t = 2 is 8 feet/second.
The correct answer choice is option A and C respectively.
What is the average rate of change?The average rate of change between t = 0 and t = 2
At t = 0
h(t) = -16t² + 40t + 6
= -16(0)² + 40(0) + 6
= 0 + 0 + 6
= 6 feet/second
At t = 2
h(t) = -16t² + 40t + 6
= -16(2)² + 40(2) + 6
= -16(4) + 80 + 6
= -64 + 80 + 6
= 22 feet/second
The average rate of change between t = 0 and t = 2 is
22 feet - 6 feet
= 16 feet/second
At t = 1
h(t) = -16t² + 40t + 6
= -16(1)² + 40(1) + 6
= -16 + 40 + 6
= 30 feet/second
Therefore,
The average rate of change between t = 1 and t = 2 is
30 feet - 22 feet
= 8 feet
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I need to know how to solve this
Answers
Answer:
x = 7
Step-by-step explanation:
4*(2x - 10) = 16
Use Distributive property,
4*2x - 4*10 = 16
8x - 40 = 16
Now, we have to isolate ' x'. To isolate 'x', first Add 40 to both sides,
8x = 16 + 40
8x = 56
Divide both sides by 8,
x = 56 ÷ 8
[tex]\boxed{\bf x = 7}[/tex]
Solve the systems by substitution.
y=4x+6
y = 7x
Answers
Answer:
x = 2
y = 14
Step-by-step explanation:
{y = 4x + 6;
{y = 7x;
.
Let's replace y in the second equation with the value given in the 1st equation:
4x + 6 = 7x
4x - 7x = -6
-3x = -6 / : (-3)
x = 2
x = 2y = 4 × 2 + 6 = 8 + 6 = 14
Q3: The standard form of (7.2 x 10)-(3.4 x 10") a) 2.14 x 10 b) 2.11 x 10 2.12 x 102 d) 2.12 x 10
Answers
The standard form of the expression (7.2 × 10⁵) ÷ (3.4 × 10³) include the following: C. 2.12 x 10².
What is an exponent?In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the law of indices for powers of the same base number and division, we have the following:
(7.2 × 10⁵) ÷ (3.4 × 10³
(7.2/3.4) × 10⁵⁻³
2.12 x 10².
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Complete Question:
The standard form of (7.2 × 10⁵) ÷ (3.4 × 10³)
a) 2.14 x 10
b) 2.11 x 10
c. 2.12 x 10²
d) 2.12 x 10
I need help on these anybody?
Answers
The complete labels to the parts of the circle such as tangent, diameter, radius and secant are found in the attchment.
What are the parts of a circle?The various parts of a circle are:
Center: The point inside the circle that is equidistant from all points on the circumference.
Circumference: The distance around the circle.
Radius: A line segment from the center of the circle to any point on the circumference.
Diameter: A line segment that passes through the center of the circle and has its endpoints on the circumference.
Chord: A line segment with both endpoints on the circumference.
Tangent: A line that intersects the circle at only one point, called the point of tangency.
Secant: A line that intersects the circle at two points.
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Calculate the total volume of Cubic Yards of Concrete needed to fill in the footer. (That is the enclosed frame in the left of the diagram above) (the footer needs to be 2 ft wide and 1 ft deep. (remember there is a 2 ft difference between the outside and the inside of trench)
Answers
The total volume of Cubic Yards of Concrete needed to fill in the footer is approximately 225.19 cubic yards.
To calculate the total volume of Cubic Yards of Concrete needed to fill in the footer, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length and height are both 20 feet since that is the size of the enclosed frame in the left of the diagram.
The width of the footer needs to be 2 feet, which means we need to subtract 4 feet (2 feet on each side) from the total width of the frame to get the inside width of the trench, which is 16 feet.
The depth of the footer needs to be 1 foot, which means we need to subtract 1 foot from the height of the frame to get the height of the trench, which is 19 feet.
Using these measurements, we can calculate the volume of the trench by multiplying length (20 feet) x width (16 feet) x height (19 feet) which gives us a total volume of 6,080 cubic feet.
To convert cubic feet to cubic yards, we need to divide the total volume by 27 (since there are 27 cubic feet in a cubic yard). Therefore, the total volume of Cubic Yards of Concrete needed to fill in the footer is approximately 225.19 cubic yards.
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Note the full question is
1) Calculate the total volume of Cubic Yards of Concrete needed to fill in the footer. (That is the enclosed frame in the left of the diagram above) (the footer needs to be 2 ft wide and 1 ft deep. (remember there is a 2 ft difference between the outside and the inside of trench)
2) What is the square footage of the footer trench ?
3) If the footer trench is 2 ft deep, would 10 Cubic-yards of concrete overfill this trench? By how much. ?
Parents wish to have $130,000 available for a child's education. If the child is now 10years old, how much money must be set aside at 3% compounded semiannually to meet their financial goal when the child is 18?
Answers
To reach their financial objective of having $130,000 accessible for their child's schooling when the youngster turns 18, the parents must set aside roughly $97,209.87 at 3% compound semiannually.
To determine how much money needs to be set aside to meet the financial goal of $130,000 for the child's education, we can use the compound interest formula:
[tex]A = P(1 + r/n)^(nt)[/tex]
where A represents the future value, P represents the principal (or initial investment), r represents the annual interest rate, n is the frequency with which interest is compounded annually, and t represents the passage of time in years.
To solve for the principal, P, in this situation, we must first identify the principal, P.
[tex]P = A / (1 + r/n)^(nt)[/tex]
Given that the child is currently 10 years old and will need the money in 8 years (at age 18), we have t = 8. The interest rate is 3%, which we need to express as a decimal (r = 0.03), and the interest is compounded semiannually, so n = 2.
Using these values and the desired future value of $130,000, we can calculate the required principal:
P = [tex]130000 / (1 + 0.03/2)^(2*8)[/tex] = $97,209.87
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The seats available to a baseball game come in four types: bleacher, box, club, and grandstand. There are 12,600 box seats and 5,400 club seats available. According to the graph, what is the total number of seats available?
Answers
Answer: 45,000
Step-by-step explanation:
Let x be the total number of seats available. According to the problem, 18% of the seats are bleachers, and 42% of the seats are grandstands. That means the remaining 40% of the seats are box and club seats combined since 100% - 18% - 42% = 40%.
The problem states that there are 12,600 box seats and 5,400 club seats available, which makes a total of 12,600 + 5,400 = 18,000 box and club seats.
Now, we can set up an equation to find the total number of seats:
0.40x = 18,000
To solve for x, divide both sides of the equation by 0.40:
x = 18,000 ÷ 0.40
x = 45,000
There are a total of 45,000 seats available at the baseball game.
A runner sprinted 103.76 yd to finish a race.
Use the table of facts to find the distance she sprinted in feet.
Round your answer to the nearest tenth.
Answers
Answer:
311.3 feet
Step-by-step explanation:
1 yard = 3 feet
Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)
Rounding to the nearest tenth gives us 311.3 feet.
The table shows the number of video games sold worldwide for the five highest-selling video games in 2010. Assuming this trend continues and that the total sales of all other video games is negligible, if a person chooses to purchase one of these video games, determine the empirical probability that the person will purchase game 2,5 and 1.
Game 1: 18,200,00
Game 2: 17,360,000
Game 3: 11,410,000
Game 4: 11,160,000
Game 5: 8,450,000
total: 66,580,000
Answers
Empirical probability of purchasing Game 1 = 18,200,000/66,580,000 = 0.273 or approximately 27.3%
Empirical probability of purchasing Game 2 = 17,360,000/66,580,000 = 0.261 or approximately 26.1%
Empirical probability of purchasing Game 5 = 8,450,000/66,580,000 = 0.127 or approximately 12.7%
Therefore, the empirical probability that a person will purchase Game 1 is about 27.3%, the probability of purchasing Game 2 is about 26.1%, and the probability of purchasing Game 5 is about 12.7%.
The empirical probability of an event is the ratio of the number of times the event occurred to the total number of observations.
So, for each game, the empirical probability of purchasing that game is given by:
Game 1: 18,200,000/66,580,000 = 0.273 or 27.3%Game 2: 17,360,000/66,580,000 = 0.261 or 26.1%Game 3: 11,410,000/66,580,000 = 0.171 or 17.1%Game 4: 11,160,000/66,580,000 = 0.168 or 16.8%Game 5: 8,450,000/66,580,000 = 0.127 or 12.7%So the empirical probability of purchasing game 1 is 27.3%, game 2 is 26.1%, and game 5 is 12.7%.
The polynomial of degree 3, p(x),has a root of multiplicity 2 at x=2 and root of multiplicity 1 at x=-4 the y intercept is -3.2
Answers
p(x) = k(x-2)^2(x+4)
where k is some constant.
To find the value of k, we use the fact that the y-intercept is -3.2, which means that p(0) = -3.2. Substituting x=0 into the equation for p(x), we get:
p(0) = k(-2)^2(4) = 16k
Setting this equal to -3.2, we have:
16k = -3.2
k = -0.2
So the polynomial is:
p(x) = -0.2(x-2)^2(x+4)
Therefore, the polynomial of degree 3, p(x), with a root of multiplicity 2 at x=2 and root of multiplicity 1 at x=-4, and y-intercept of -3.2, is given by:
p(x) = -0.2(x-2)^2(x+4)
Naomi wants to wrap a gift for her sister. The gift is in a box with a length of 10 inches, a height of 2 inches, and a depth of 3 inches. If Naomi is calculating the minimum amount of wrapping paper to wrap the gift, would she be finding the Volume or Surface Area?
Answers
To calculate the minimum amount of wrapping paper needed to wrap the gift, Naomi would be finding the Surface Area.
The Surface Area of a three-dimensional object is the sum of the areas of all its faces. In this case, the gift is a rectangular prism with dimensions of length 10 inches, height 2 inches, and depth 3 inches.
To wrap the gift, Naomi would need to cover all six faces of the rectangular prism with wrapping paper. The formula for the Surface Area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, h, and w are the length, height, and width of the rectangular prism, respectively.
Substituting the values for the length, height, and depth of the gift, we get:
Surface Area = 2(10 x 2) + 2(10 x 3) + 2(2 x 3)
Surface Area = 20 + 60 + 12
Surface Area = 92 square inches
Therefore, Naomi would need at least 92 square inches of wrapping paper to cover the gift, which is the Surface Area of the rectangular prism.